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The Period in the Volterra–Lotka Predator-Prey Model

1983; Society for Industrial and Applied Mathematics; Volume: 20; Issue: 6 Linguagem: Inglês

10.1137/0720098

1095-7170

Jörg Waldrogel,

Fractional Differential Equations Solutions

The Volterra–Lotka predator-prey differential equations ${{dX} / {dt}} = aX(Y - 1),{{dY} / {dt}} = - bY(x - 1)$ possess a one-parameter family of periodic solutions. The period P of these solutions is investigated. By means of a suitable transformation P is represented as the integral over a full period of an easily computable real-analytic periodic function. Hence the trapezoidal rule provides an efficient algorithm for the numerical calculation of P. Furthermore, an asymptotic expansion for large values of P is derived by means of inverse Laplace asymptotics.